III. Evaluate using simple divergence test cos(n7) п 6. n=0 2(n +1) Зп - 1 7.

Q: 1. Use the Nth-Term Test to examine the divergence of: n n+1 n=1

A: Follow the steps and just remember the form of the nth tems test.

Q: dt converges. There is no value of r such that (3t)-" 14.

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Q: Ex:@ Suppose thet the tallowing transformutioun Conneciãs the (x') and (xi) cordnate ار ک هأولاS…

A: Question: The transformation is T=x¯1=ex1+x2x¯2=ex1-x2 Calculate: (1) The jacobian matrix J and J-1…

Q: 1 (x + 1)2 dx -2

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Q: 1- Fird the extreme va lues of the funetion and where the inter val S on whi'ch de eveensing and…

A: As per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost…

Q: If Osf(x)s g(x) on [a, ∞) and | g(x)dx is divergent, then | F(x)dx is divergent. Select one: O True…

A: We have to state true or false.

Q: Using the nth term test for divergence, the series 00 > V52n+1 an %3D n=1 n=1 is divergent since lim…

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Q: H) 9f zyzec then prove thal nl x=4=Z, (alogen) %3D

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Q: 3. Recall that x - Poisson(0) = Mz(t) = e"(e*-1). %3D A. Derive the MGF of Z = (F - 0)/ /0/n where F…

A: Please find the solution below. Thank you.

Q: 2. If :|S1, determine the maximum modulus f(:) (a) f(=) =z-2z+3, (b) f(=) == +z-1, (c) f(=)3= :+1…

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Q: Find the divergence of = ea + sin(xy) a + cos² (xz) a X O yey+x cos(xy) - 2x cos(xz) sin(xz) ọ xe…

A: U→=exyax+sin(xy)ay+cos2(xz)az

Q: Q11 Determine all the critical points for the following- S(x) = sin'x- cosx On the interval (0, 2n).

A: Given , f (x) = sin2x - cos x  (.) Definition :  Then critical point of a…

Q: 1 Consider the diffe dy - y² +4y³ - 12y² a) What are the equilibria? b) On what intervale) is…

A: As per our guidelines we are supposed to answer only 3 sub part. Here first three subpart answered.

Q: 14. k=1 2k

A: Given query is to test the series using divergence test.

Q: 4.) Suppose X has moment generating function MX(t) = 0.3e−t + 0.1 + 0.1et + 0.2e2t + 0.3e3t. What is…

A: It is an important part of statistics. It is widely used.

Q: X1, ., Xn are idd. find the MLE and cramer rao lower bound for unbiased estimator for theta. f (x |…

A: Given  fxθ=θ              when x=-11-θ2θx     for x=0, 1, 2, ....

Q: (a) Show that the moment generating function of X is given by 1 Мx() - 1<t< 1. 1 – t2

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Q: 00 Σ 3n° +1 n=0

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Q: Σ-νω( ) 8. (-1)" sin n=1 Input C for convergence and D for divergence:

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Q: Find the divergence of U = r cos 0 a, - sin 0 ag + 2r² sin 0 2 sin 0 3 sin 0 - r2 2 cos 0 3 cos 0 r2…

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Q: Find the divergence of U = r cos 0 a, – sin 0 a, + 2r² sin 0 ap. r 2 sin 0 3 sin 0 - r2 None of the…

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Q: cos“ n Σ 48. n2 n=1

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Q: 1/x e 7 dx y3 -1

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Q: f fn → ƒ uniformly and the functions fn have only jump discon- sinuities, prove that f has only jump…

A: Here we use epsilon delta proof

Q: Discuss the Convergence or Divergence for D { [4+ (-0"]" (Z+2)" こう 2n+1 - DZ² 2 لع Wi ngo (2n+¹)!

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Q: Use the Chain Rule to find az/as and az/at. sin(0) cos(p), 0 = st7, p = s³t əz t³cos(p) cos(0) —…

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Q: 00 6n–1 Зп+2 1 Apply the nth term divergence test to conclude if E converges or diverges.

A: The divergence of a series can be found using the nth term test. Consider the series . Let . If…

Q: Q5) Evaluate the integral 0.61-10 (6.73x + 4.3025 - 10- dx 2.316 • 10-11 122-10- Using trapezoidal…

A: The solution to the integral can be calculated using numerical methods. The formula for the…

Q: Find an upper bound for the Lagrange interpolation error for f(x) sinh(x)+2 cosh(x) over the…

A: Given: fx=sinhx+2coshx, x∈0,2. Interpolation nodes xk=k4, k=0,1,⋯,8. To find:          An upper…

Q: Is xo is an ordinary point of the ODE? If so expand p Find a minimum value for the radius of…

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Q: sin(²) En=1 is 18 √n a. 1 b. 12/12 c. Converge d. Diverge d O C O a O b O

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Q: that you you used to det divergence. 3 n (1). E n5+3 n=1 (1). Σ n 2" n=1

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Q: az az and as Use the chain rule to find at (=) Z = tan V u = 8s + 5t, v = 5s – 8t az as az at

A: Topic:- derivatives

Q: 2 Q/if the function fc)=ĕ is not Continuous at T where =TIL x<T foint the fourier Scries of fcxeě is…

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Q: the series %3D an V52n+1 n=1 n=1 is divergent since lim an= %3D n- +o 16 This option O This option…

A: 5^lim(2n+1)/(n)=5^2=25.

Q: CoS“ n In n а. n2 n³ n=1

A: Solution: a) ∑n=1∞cos2(n)n2+ln (n)n3

Q: 9n + 2" 46. Prove the divergence of n=0

A: Given series  ∑n=0∞9n+2n5n where an=9n+2n5n.

Q: Calculate the divergence of cach of the following functions (a) r²î + y²§ + 2²k. (b) yzî + xzj+ xyk.…

A: As per the instruction, we will answer only the first 3 subparts. For (a), For a given vector fx, y,…

Q: 1. Calculate the second moments in time and frequency around time zero and frequency zero,…

A: Given: The function st=e-t22   To calculate: The second moments in time and frequency around time…

Q: Suppose f(x) > 0 and g(x) > 0 and that | f(x)dx diverges. If f(x) > g(x), what can we conclude about…

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Q: Which of the following graphs is the slope field for 15/1 1~/1ST ~\~ in 13t-ii-i ~~~ -1 1 2 3 4 5…

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Q: Using the Nth term test for divergence, 00 n 5n-2 n2 n=1 diverges since lim V5n-2 n² is equal to O 5…

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Q: -5 1 10) Determine whether the improper integral diverges or converges: ī dx Vx-1

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Q: Defn `x;>-` "x; diverges to minus infinity" VR>O such that Vj >Ng *;<-R NR HWs If x→0 then → O.…

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Q: -4 After evaluation, Jo dx tends to be 0 x2-9 A. convergent B. divergent C. insurgent D. allegiant

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Q: メー) whatis theradius h.gh of convergense f the power senes) 9.3 b. 2

A: ∑n=1∞(x-1)nn.3nwe have to find radius of convergence of the power series

Q: Which of the following graphs is the slope field for dx 12 -3-211. s 2 13 US 111-2-/35 1112 111²-111…

A: Here we have to solve the given differential equation and plot the solution

Q: 1- Find dwi dt at the given value for w ==+2,x = cos (1), y = sin (1),z = w =-+ at = 3

A: